Part V · 3 — Map of the sciences

draft

A "by science" view: for each discipline, where it enters the life cycle and in which types of AI it is most central. Complements the matrices (doc 2), which are "by step."

Mathematics

Discipline Where in the cycle Types where it is central
Linear algebra Modeling, Training, Production almost all connectionist ones
Calculus / analysis Training, Retraining neural networks (backprop)
Optimization Training, Retraining deep learning, RL, evolutionary
Probability all Bayesian, diffusion, VAE, HMM
Statistics Data, EDA, Evaluation, Monitor. classical ML, evaluation of everything
Information theory Modeling, Training VAE, diffusion, compression, RAG
Geometry / topology Modeling embeddings, video, robotics
Graph theory Modeling GNN, planning, knowledge graph
Groups / symmetries Modeling CNN, GNN, equivariant models
Combinatorics / complexity Problem, Homologation planning, solvers
Mathematical logic Problem, Homologation, Governance symbolic, neuro-symbolic
Stochastic processes Training, Monitor. diffusion, HMM, RL, SSM
Control theory Monitor., Retraining continuous RL, robotics, SSM, agents
OR / queueing theory Production serving, recommendation
Game theory Problem, Modeling GAN, AlphaZero, recommendation, agents
Numbers / cryptography Governance privacy, security

Natural and engineering sciences

Discipline Where in the cycle Types / role
Physics Modeling diffusion (statistical mech.), robotics, quantum computing
Neuroscience Modeling network inspiration, attention, memory
Biology / evolution Modeling, Retraining evolutionary, neuroevolution, swarm
Electrical / electronic eng. Training, Production all the hardware (GPUTPUNPU)
Materials science / chemistry Training, Production semiconductors; GNN (molecules)
Acoustics / optics / DSP Data, Modeling, Production audio, speech, music, vision, video

Humanities and social sciences

Discipline Where in the cycle Types / role
Cognitive science Problem, Modeling reasoning architectures, agents
Psychology / psychometrics Evaluation, RLHF benchmarks, reinforcement, annotation
Linguistics Data, Modeling LLM, ASR, TTS, RAG, multimodal
Economics / game theory Problem, Production recommendation, auctions, multi-agent RL
Philosophy / ethics / epistemology Problem, Governance alignment, neuro-symbolic, decisions
Law / regulation Data, Governance privacy, copyright, compliance
Sociology / anthropology Data, Governance bias, impact, fairness
Music theory / arts / color Data, Modeling music, image, video (artistic modes)

Reading the map

  • The common base (linear algebra, probability, optimization, statistics) is

    required by almost every type of AI — it is the "trunk."

  • The modality sciences (acoustics, optics, linguistics, music theory) come in

    according to the type of data.

  • The paradigm sciences define the "school": logic→symbolic,

    biology→evolutionary, control→reinforcement/robotics, economics→recommendation.

  • The humanities concentrate at the ends of the cycle (Problem and Governance) —

    the "why" and the "may we?".